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Notes on Minimax, Maximin and Maximax

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Notes on Maximin, Maximax and Minimax (Regret criterion)

  • Used when probabilities of events are unknown
  • Based on the attitude of the investor

Maximin

  • Investors aim to maximise minimum return, hence the name Maximin.
  • Under this method the decision maker assumes the worst possible outcome and hopes to maximise that outcome, thus chooses the largest pay-out under the “worst” circumstances
  • It is a pessimistic approach

Maximax

  • It is a more optimistic approach
  • Investors seek to maximise the maximum return hence the name Maximax.
  • Under this method decision maker will assume the best outcome and seek to maximise it

Minimax or Regret Criterion

  • This is a more neutral approach
  • Under this approach the decision maker simply aims to minimise maximum regret hence the name minimax.
  • This regret could be defined as the financial gain between different outcomes, and can be identified using opportunity costing

Example

Peter is a budding entrepreneur who is interested in starting a one of a kind digital technology business, he is torn between two high end machines that he could possibly use. however due to a lack of such firms in the market, the uncertainties that would affect the demand of the service is difficult to predict. The following are the possible outcomes

Recommend a decision based on the use of the Maximin, Maximax and regret criteria approaches.

 Income generated by the use of machines under different events

High demand ($)

Low Demand ($)

Machine A

100,000

70,000

Machine B

250,000

10,000

Under Maximin, the decision maker here Peter will assume the worst outcome will occur and try to maximise the return of such a situation, thus under low demand

Assuming low demand, he sees that

Machine A shall provide a turnover of $70,000 and Machine B a turnover of $10,000

Peter shall choose to use Machine A

Under Maximax, the decision maker here Peter will assume the best outcome will occur and try to maximise the return of such a situation, thus under high demand

Assuming high demand, he sees that

Machine A shall provide a turnover of $100,000 and Machine B a turnover of $250,000

Peter shall choose to use Machine B

Under Minimax, the decision maker here Peter will try to minimise maximum regret.

To do this we must make a regret table by looking at the initial schedule

High demand ($)

Low Demand ($)

Machine A

100,000

70,000

Machine B

250,000

10,000

Regret Table

High Demand

Low Demand

Maximum Regret

Machine A

150,000

0

150,000

Machine B

0

60,000

60,000

Under this Peter would want to minimise his maximum regret so he would choose to go with Machine B as the maximum regret is lower than the regret of choosing Machine A.

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